You're so right. Just look at the reaction when Chris Moyles left R1, or Christian O'Connell left Absolute the other week - people really cared. Listeners get really invested in shows and the people on those shows. It's what makes radio so special, it's a very personal medium and you feel like you know the people involved so only natural to feel like it extends beyond a three hour radio show.
I don't think it's at all weird. I think it's quite natural - especially if you listen to them every day and have done so for years. They share so much of their lives and you become invested; look at when Chris Stark announced he was getting married. That was a huge moment for me as a listener as I have listened to Scott and Chris for years - from the Tap End days and the stag dos/holidays in Kavos to this big thing.
Have to say, I'm a bit jealous watching all the Instagram stories of the Radio 1 DJs right now. They're all out in Swansea and it looks like they're having such a laugh, is it weird that I'd love to be mates with them.
Chris Stark and Jordan's are particularly good, they've filmed Matt Edmondson and Molly King riding off on scooters ditching them. It's very funny.